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# Double Digit Multiplication and the Area Model

Lesson 11 of 19

## Objective: SWBAT multiply double digit by double digit numbers using an area model.

## Big Idea: Students discover how to apply prior knowledge to solve a double digit multiplication equation using an area model.

*50 minutes*

#### Warm up

*10 min*

**Math Zapper Ap**

Today, I wanted my students to work on their multiplication facts and have a little fun at it. We warmed up on an ap on their iPad called Math "Zapper". It's from "Math Blaster." It is fun because they can set their space ship to the pace and to the level of facts. I gave them about 10 minutes of fun to work on their multiplication or division facts.

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This lesson is short and to the point.

Today, I presented this lesson to the whole class because all of my students did not master double digit by double digit multiplication on the multiplication pre-test. I wanted to see if they could apply prior knowledge of multiple digit by one digit multiplicaiton to figure out how to multiply the double digits by double digits. I wondered if they would figure out on their own to create an area model and break apart each number using expanded form and place value to multiply.

I used my Smart Board Notebook file to drive their thinking. They used their paper notebooks to do their figuring in as I opened up the lesson. Double digit multiplication/ estimation. The first slide encourages them to think about what they already know in order to figure out how to solve a double digit multiplication problem. Teacher Effectiveness rubrics encourage us to allow students to develop their own thinking and processes by us encouraging them to apply prior knowledge. This independence I have allowed should help them realize that they are problem solvers! This sample of an attempt at how to do 2x2 digit multiplication shows how my students tried to figure out on their own, what process we would use to solve a double digit by double digit algorithm (2x2 digit).

I began to instruct the whole class lesson using the resource of a Learnzillion Lesson as they took notes. This video resource was particularly helpful as it was presented just as I would present area models. It gives them a chance to listen to someone else instruct as I monitored their attentiveness and focus. I then had them practice several notebook 2x2 multiplication problems before I assigned them their homework. Because my students are one on one iPad, they also can use the Learnzillion resource to help them with their homework at home.

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#### Practice Work and Assignment

*15 min*

For practice, I assigned Homework and Resources IXL.com D.11. This online application is really great for many reasons.I like it for the convenience of having it online. With students and one on one iPads, it replaces a textbook, or copies of worksheets. My students were instructed to show all work on their papers and solve using area models. We discussed if one factor was tens, that they just need to write it sideways and multiply using their basic fact and their knowledge on how to think about multples of ten.

When they answer incorrectly, the correct calculation pops up. I expect them to figure out what they did wrong and show that work on their paper. This assignment, however does not show any area model when they answer incorrectly. It brings up the standard algorithm. Therefore, I told them to ignore that and look to find the errors within their area model. I asked them what they would look for.

The first thing that popped out of their mouths was to look at the partial products and their multiplication of tens. The second thing was that they probably added the partial products wrong. One student mentioned that they multiplied their basic facts wrong.

I am glad to see that the thinking has transferred from their area model lessons on 1 x up to four digits. This is really great to see!

I allowed them to get started with 5 or more problems. At home, I assigned at least 20 minutes of practice. I logged on later in the evening to check progress. The program shows me how many they did and the level of mastery. I can already see who didn't do their homework and who didn't master it. If no internet is available at home, I have a supplemental worksheet. This worksheet was from Scott Foresman Publishing. They did not need to estimate to check their work just yet. All of my students used IXL.

#### Resources

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pretesting The Multiplication Unit
- LESSON 2: Introduction to Area Models
- LESSON 3: Area Models: Extension of Understanding
- LESSON 4: Area Models: 4 Digit by 1 Digit Multiplication
- LESSON 5: Getting Ready to Quiz: The Greatest Product Game
- LESSON 6: Quiz 1 in Multiplication: Area Model fluency 1x2,1x3 & 1x4 digits
- LESSON 7: Estimation of Products Using 1 Digit up to 4 Digit Equations.
- LESSON 8: Multistep Word Problems, Algebraic Concepts & Equations: Strategy Toward Mastery!
- LESSON 9: Quiz 2 : Multiplication Word Multi-Step Problems: 1x2,1x3,1x4 digit and estimation
- LESSON 10: An 1870's Classrom Meets Common Core: Drilling Math Facts & a Game of What's Wrong with This Answer?
- LESSON 11: Double Digit Multiplication and the Area Model
- LESSON 12: Powers of Ten: Review and Practice and Writing Clear Explanations
- LESSON 13: Multi-step word problems: Review and Support to Mastery
- LESSON 14: Quiz 3: Double Digit Multiplication, Estimation and Solving Word Problems
- LESSON 15: Estimating Double Digit by Double Digit Multiplication
- LESSON 16: Reviewing for Multiplication Assessment: A student jigsaw presentation.
- LESSON 17: RTI: Making Solving One Step Word Problems a Piece of Cake!
- LESSON 18: Estimation Scenarios: Writing Estimation story problems.
- LESSON 19: Assessing Multiplication